Most children eventually memorise their times tables one way or another. The question Montessori asks is different: does a child actually understand what multiplication means, or have they just memorised a grid of answers that will fade the moment recall pressure eases?
Multiplication as Repeated Groups, Physically
The bead bar material represents each number, one through ten, as a coloured bar of that many beads. Multiplication starts as a physical act: "four times three" means laying out four bars of three beads and counting the total. A child does this repeatedly, with different numbers, until the pattern of repeated groups becomes intuitive, not just a fact recited from memory.
Why This Order Matters More Than Speed
Traditional times-table drilling optimises for one thing: fast recall. Montessori optimises for something that speed alone can't provide, an understanding a child can rebuild from scratch if a fact is forgotten. A child who understands multiplication as repeated grouping can reconstruct "7 x 8" even on a day their memory fails them, by working from 7 x 7 (which they might recall) and adding one more group of seven. A child who only memorised the grid has nothing to fall back on.
The Checkerboard for Multi-Digit Multiplication
Once single-digit multiplication is solid, the checkerboard material extends the same physical logic to multi-digit problems like 24 x 13, using place-value columns and coloured bead quantities laid out on a large grid. A child physically builds the answer to a large multiplication before ever being shown the standard written algorithm, so the algorithm, when it's finally introduced, is explaining something the child has already done with their hands.
Division as the Inverse Operation
Division follows the same physical logic in reverse: a total quantity of beads is shared equally into groups, and the child discovers how many go into each group or how many groups can be made. This concrete "sharing" experience is why long division, often one of the most mechanically confusing algorithms taught in primary school, tends to make more sense to Montessori-taught children when it's finally formalised.
Conclusion
Multiplication and division memorised without understanding are fragile: reliable until the moment memory fails, and useless after that. Built from physical, repeated grouping first, they become something a child can reconstruct, not just recall, which is the whole point of how this work happens in our Primary Maths and Elementary Maths courses.
Book a trial class to see a bead bar or checkerboard lesson in action.
Sources
- Association Montessori Internationale (AMI), for the reference multiplication and division material sequence.
- National Council of Teachers of Mathematics (NCTM), on conceptual understanding versus rote memorisation in arithmetic instruction.